Is this nosie is similar to nosie what produce chaning from N to R or from R to 1?
More, I hear two "clicks" then shifting from N to 2d gear (mean, using D with 1st mode it shifts to 2d gear instantly).
The same noise I hear sometimes from downshifting from 3d to 2d, or during moderate (not quite) breaking in D-mode then it downshifts to 2d and to 1st gear...

This sounds worry me very much, I don't know if it is normal or this can be solved?
I have askd for my BMW service, but they don't have any good expirencie on new M3...

The transmission and diff are very much like the previous model's, or those of the M5/6, so drivetrain noise analysis should not be new. No, the sound is totally different, like the rear wheel is rubbing on the wheelwell liner in a tight turn.